The reliability of hourly PM2.5 data obtained from air quality monitoring stations is compromised as a result of the missing values, thereby impeding the thorough examination of crucial information. In this paper, we present a spatiotemporal (ST) stacking machine learning (ML) method with daily-cycle restrictions for reconstructing missing hourly PM2.5 records. First, the ST neighbors for the target station with missing values are selected at a daily scale. Subsequently, the non-null data within the ST neighbors undergo an iterative P-BSHADE interpolation process for re-interpolation. Next, a stacking ML model is constructed using the re-interpolation values and several environmental factors associated with PM2.5 as the predictors, while the observed PM2.5 is taken as the independent variable. Finally, the missing values are reconstructed by inputting the predictors into the trained stacking model. The study utilized hourly PM2.5 data in the Beijing-Tianjin-Hebei region as a case study to assess the effectiveness of the proposed method, using daily missing ratios of 10%, 30%, and 50%, respectively. The accuracy of the proposed method was then compared to four contemporary ST interpolation methods. The results indicate that the proposed method exhibits superior performance compared to the classical methods. Specifically, it achieves a reduction in the average root mean square error and mean absolute error by at least 40.6% and 40.1%, respectively. Additionally, the proposed method demonstrates the successful recovery of extreme values in the hourly PM2.5 records, in contrast to the classical methods which often exhibit a tendency to overestimate low values and underestimate high values. Overall, the proposed method presents a viable and efficient approach to recover missing values in the hourly PM2.5 records that demonstrate evident daily periodic patterns.

中文翻译：

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具有日周期限制的时空叠加方法重建缺失的每小时 PM2.5 记录

空气质量监测站每小时PM2.5数据的可靠性因缺失值而受到影响，从而阻碍了对关键信息的彻底检查。在本文中，我们提出了一种具有每日周期限制的时空（ST）堆叠机器学习（ML）方法，用于重建丢失的每小时 PM2.5 记录。首先，在每日尺度上选择具有缺失值的目标站的 ST 邻居。随后，ST邻居内的非空数据经历迭代P-BSHADE插值过程以进行重新插值。接下来，使用重插值和与 PM2.5 相关的几个环境因素作为预测变量，构建叠加 ML 模型，同时将观测到的 PM2.5 作为自变量。最后，通过将预测变量输入到经过训练的堆叠模型中来重建缺失值。该研究以京津冀地区每小时的 PM2.5 数据作为案例研究，以日缺失率分别为 10%、30% 和 50% 来评估该方法的有效性。然后将所提出方法的准确性与四种当代 ST 插值方法进行比较。结果表明，与经典方法相比，所提出的方法表现出优越的性能。具体来说，它的平均均方根误差和平均绝对误差分别降低了至少 40.6% 和 40.1%。此外，所提出的方法证明了每小时 PM2.5 记录中极值的成功恢复，而经典方法往往表现出高估低值和低估高值的倾向。总体而言，所提出的方法提供了一种可行且有效的方法来恢复每小时 PM2.5 记录中的缺失值，这些记录显示出明显的日常周期性模式。